RELATIVE POSITIONS OF LATERAL MEMBERS. 
199 
three rows, so that each new division-wall of the apical cell is parallel to the last 
division-wall but two, as in Fonlinalis, three rows of leaves result, arranged spirally 
with the constant divergence \. When the apical cell is a three-sided pyramid, 
but the new walls which are formed in it are not parallel to those already in existence, 
but oblique, so that, for example, all the segments are broader on the anodic than 
on the kathodic side, then the segments no longer lie in three straight rows, but 
either three spirals or one only can be recognised encircling the axis; and since each 
* segment ' in this case {e. g. in Polyirichum, Calharinea, and Sphagnum ^) developes 
into a leaf, the leaves are formed in spiral phyllotaxes, with divergences depending 
on the obliquity of the principal walls of the segments to one another^. These 
phenomena show clearly that when each segment produces a leaf, the phyllotaxis 
depends on the manner in which the new principal walls of the segments arise ; and 
since the direction taken by the segmentation of the apical cell depends again on 
causes of which we are at present ignorant, the phyllotaxis must also finally be 
referred to these unknown causes. In certain cases a reason may be given why, when 
the mode of segmentation of the apical cell is the same, the positions at which thj; leaves 
are formed are nevertheless variable. The segments of the apical cell, both in 
Fontinalis and in Eqinseium, lie in three straight rows ; but in Foniinalis the solitary 
leaves stand in straight rows and are arranged spirally with the constant divergence 
I, while in Equiseiwn^ on the contrary, alternating whorls of leaves arise which have 
grown together in the form of a sheath ; because here, as Rees has shown ^, the three 
segments of each cycle, arranged originally in a spiral manner, are finally placed, in 
consequence of the growth not being uniform, on the same zone. From this a cir- 
cular projection next grows out, on which the sheath-teeth are formed. From the 
want of uniformity in the growth of the segments, the causes of which are at present 
unknown, still further differences, as compared with Fonihialis, are introduced, in 
consequence of which the development of the whorls themselves becomes alternate 
instead of superposed, as might be the case. If the processes which take place in 
Marsilea, as Hanstein has described them ^ are compared with this, it is seen that the 
segmentation of the apical cell of the stem agrees in the main with that of Fontinalis 
and Equisetum ; it is in three rows with a divergence \. As in Fonfinalis, the leaves 
originate by a curving outwards of the segment-cells ; but the leaves are in this case 
not arranged in three rows as in Fontinalis, nor in whorls as in Equisetum, but in two 
rows. The immediate cause of this must be sought in the fact that the stem, together 
with the growing point, lies in a horizontal position ; it has an upper and an under 
side. The segments of the apical cell form two rows on the upper and one on the under 
side ; but the former produce leaves, the latter roots. The horizontal position of the 
stem and its bilateral development are here perhaps the cause why the upper side 
^ Compare the admirable description by Leitgeb in the case of Sphagnum, in the Sitzungsber . 
der kais. Akad. der Wissenschaften, Wien, March 1869. 
^ See Hofmeister, Allg, Morph, p. 494; and Müller, Eine algeineine morphologische Studie, 
Bot. Zeitg. 1869, t, IX. fig. 24. In such cases the behaviour of the apical cell may be represented by 
imagining it to rotate on its axis, as I expressed it in my first edition. The description there given 
does not however now appear to me suited to the beginner. 
^ Rees, Jahrb. für wissen. Bot. vol. VI. p. 216. 
* Hanstein, in Jahrb. für wissen. Bot. vol. IV, p. 252. 
